The Knapp–Stein intertwining operators are a major tool in harmonic analysis of \(G\)  (as of any semi-simple Lie group, see, e.g., [1]}). For \(\lambda \in \mathbb {C}\)  and \(f\in C^\infty (S)\) , let
\(I_\lambda f(x) =\frac{1}{\Gamma (\lambda -\frac{n}{2})} \int _S \vert x-y\vert ^{-2n+2\lambda } f(y) dy,\) 
